The Boris algorithm is the most popular time integrator for charged particle motion in electric and magnetic force fields. It is a symmetric one-step method, and it preserves the phase volume exactly. However, it is not symplectic. In this talk we prove near-conservation of energy over very long times in the special cases where either the magnetic field is constant or the electric potential is quadratic. When none of these assumptions is satisfied, it is illustrated by numerical examples that the numerical energy can have a linear drift or its error can behave like a random walk. This work is based on an article with the same title (co-authored with Christian Lubich) that is submitted for publication.